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Preprint Number 511

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511. Rahim Moosa and Anand Pillay
A model-theoretic perspective on algebraic reductions of hyperkaehler manifolds

Submission date: 9 October 2012.


A model-theoretic abstraction and treatment of the material in Section 2 of [Campana, Oguiso, and Peternell. Non-algebraic hyperkaehler manifolds. Journal of Differential Geometry, 85(3):397--424, 2010] is given. The property of a finite rank type having all nontrivial fibrations almost internal to a given invariant set of types is introduced and explicated. As a consequence, on the complex-analytic side, it is shown that the algebraic reduction of a nonalgebraic (generalised) hyperkähler manifold does not descend.

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Full text arXiv 1210.2793: pdf, ps.

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